Monday, 6 July 2015

Apurvata, Antarabhava & Backus Naur Part I

I am writing this as an initial response to the following comment on my previous blog entry-

Could you kindly post about the relationship between Panini's grammar and the Backus–Naur Form? Cheers.

Every language, at some time or another, has claimed supremacy on the grounds of some supposedly unique quality it possesses.

My ancestors certainly thought Sanskrit and Tamil were special but, since they admitted that deaf people could gain Gnosis, they did not develop a chauvinistic mentality like that of the Nazi, Heidegger, who claimed that German was the language in which Being thinks itself.

Over the last four or five decades, the great expansion of job opportunities in Software engineering has meant that particularly risible claims have been made regarding Paninian Sanskrit.

This extract from a Time of India article is by no means the worst offender-

 The human-programmable computer languages that exist today, say C++ or Java or Ruby, can be described precisely in a few hundred rules. This precision allows these languages (and Paninian Sanskrit) to be lexically analyzed by a parser, which can then create a semantic tree structure that encodes the underlying 'meaning' of the statement (or program). That semantic tree can then be translated precisely into machine code (binary, ie 0 and 1, or hexadecimal, ie 16 characters, 0123456789ABCDEF) which will then run on the machine.The above is what compilers do – the programs that translate human-readable languages into the incomprehensible machine code (or slightly less obscure Assembly Language) that machines can understand. I worked on compiler construction for several years, and they are among the most sophisticated software in regular use.
'So what exactly does "context-free" mean? It means that the meaning doesn’t depend on contextual knowledge or common sense. Obviously human languages are context-sensitive: you just have to know certain things as a user of the language or else you will be confused. Here is an example of two sentences in English:
1. Fruit flies like an apple
2. Time flies like an arrow
'The two sentences are lexically identical, but to the human reader, based on contextual knowledge, they are vastly different. But to a computer, which has no context, they are identical. If the computer is fed the first and told that fruit flies are a kind of fly and that apples are fruits, it will create certain semantic model. Then, when given the second sentence, it will conclude that 'time flies' are a kind of fly and that arrows are fruits!
'It is essentially impossible to write such ambiguous sentences in Paninian Sanskrit. That is one of the reasons why word order doesn't matter in Paninian Sanskrit, as it does in English (imagine "Rama killed Ravana" and "Ravana killed Rama" as examples).
'That someone millennia ago was able to conceptualize, and even more astonishingly, create a Grand Unified Theory of Language is simply stunning. Let us note that even a widely acknowledged genius like Albert Einsten failed to come up with a Grand Unified Theory of Physics, even though he tried hard. Arguably, Panini’s successful effort then was the greatest accomplishment of a single mind in all of recorded history: creating something so advanced that it took 2500 years to figure out how to use it!'

Older languages- like Latin 0r Old English- tend to be highly inflected and thus word-order doesn't matter. However the corruption of a single morpheme radically changes meaning so, in practice, both increased redundancy and loss of inflection feature in the evolution of Language.
Paninian Sanskrit wasn't different from other Synthetic languages. However, it evolved on a less synoecist fitness landscape and empowered intellectuals irrespective of their geographic location. Sill, there were 'collocational availability cascades' based on superior aesthetic status accorded certain paradigmatic works. Thus, in practice, Sanskrit literature appears as if it it were the univocal expression of a single, timeless, Imperium or Oikumene. Some learned authors continued to exploit its infinite semantic potential- by devices like  vakrokti (indirect expression) or slesha (double meaning) - for example by writing texts which carry forward two wholly unconnected narratives (bahurasyakavya). However, this has tended to be seen as a blameworthy departure from the simplicity and naturalness of true poetry.

In other words, Sanskrit- thanks to Panini- is much more ambiguous, at least potentially, not less so, than other synthetic languages.
Ambiguity means that there is more than one possible meaning. Human beings can't communicate without ambiguity. Why? They have intentionality. In other words, they intend something not present which, on analysis, is fuzzy even to themselves.
If I say- 'My hand is on fire.' I might mean that I have got a good set of cards, or that I am painting really well today or that  I feel a burning sensation in one of my limbs.
Things become more clear cut, unless I am being rhetorical, if I add the following three sentences, 'Pick up the fire extinguisher. Direct the nozzle at my hand. Release the foam by pulling the trigger.'
Is there any ambiguity left in the string of sentences I have uttered? Wouldn't every ambiguity be cleared up if enough supplementary sentences were added?
Surely, Language is just a tool and, as the more extreme of the Logical Positivists suggested, any statement that isn't purely factual (e.g. my hand is on fire) or imperative (e.g. pick up the fire extinguisher) or mixed ('Release the foam by pulling the trigger' isn't wholly false just because the trigger is actually released by squeezing not pulling) is simply poetic nonsense or mystical mumbojumbo?
The answer, I am afraid, is that everything depends not just on my intentions and what I assume to be your intentions and to a possible contract curve between us, but also to a possible 'overlapping consensus' between us regarding both Facts and Values in possible future states of the World. However, if Knightian Uncertainty obtains, future states of the world can't be differentiated without ambiguity.
Why is it that, in the real world, we say things like 'Fuck, my hand's on fire, get the fire extinguisher for God's sake'. The obvious answer is-the word 'Fuck' conveys urgency as well as sense of camaraderie. 'God's sake' implies that you have a duty to the Creator to protect the life of one of His Creatures. However, using words whose meaning is essentially ambiguous or even omnivalent, signals something else- viz. we are not sending a coherent message at all because we can't currently afford the computational cost of clarifying it. In this case our utterance points to, without naming, the default focal point for communication's co-ordination game.
What if we were robots without any theory of mind? What happens when our sensor picks up a character string? 
There are 2 possibilities. Either the character string is noise in which case it is disregarded, or it satisfies a certain protocol in which case further protocols regarding authorization, priority, feasibility etc. have to be fulfilled before anything happens.
Notice that at each stage the signal is ambiguous w.r.t. reception- either it is noise or it is not noise, either it is authorized or it is unauthorized etc. This ambiguity can be reduced by devoting more Computing power to the signal. Even if computing bore zero cost, ambiguity would not disappear because- by a corollary of Razbarov-Rudich- there is no way of distinguishing pseudo-random from truly random stings (unless P=NP has a proof using current methods). 
As a matter of fact, computing is costly and, what's more, the type of  Concurrency and Race Hazard problems specific to this field soon become intractable.  But this is what we would expect to happen if Life evolved. Individual brains exist because Ambiguity is everywhere and so heterogenous trade-offs must be made at the individual level so that there is an Evolutionarily Stable Equilibrium on a higher scale.
Let us drop the supposedly simplifying assumption that we are 'basically' mindless robots because it involves an Open Question for Maths. What happens when we make the opposite assumption- viz. that that, for a philosophically advanced enough member of our species, unambiguous Reception is possible? This is equivalent to the claim that some human mind can have certainty re. what he knows and/or how he came to know it. In Sanskrit, this is covered under the rubric of Prakaasha and Praamaanya respectively.
The claim that sentences in Paninian Sanskrit are unambiguous implies that they can be 'svatograhya'- i.e something empirically received (because it is heard)  yet apprehended as intrinsically true at the same time as it is cognized.  This is a much more reasonable claim than that any sentence in any language could have this property. After all, back then, a guy who was speaking to you in Classical Sanskrit probably wasn't an idiot or a babbling drunkard but a respectable person careful with his words. Still, no Indian thinker was so foolish as to say that anything said in proper Skt. must be true. On the contrary, Religions like Jainism and Buddhism used Paninian Skt. to guard against commentary being taken for Revealed Text. In other words, Prakaasha/Praamaanya theory promotes the notion that Language is not just instrumental but strategically so- it is gamed as part of a wider lila- or sportive play of Gnosis.

Interestingly, there is a convergence between Sanskrit Literary Theory and the modern study of 'formal languages' in certain respects. In the former, aporias regarding Prakasha/Praamaanya gave salience to 'Dhvani' theory which highlights the freedom and creativity of the receiver, not the sender, of the signal. In the latter, Turing, on Bearnay's suggestion, had to take recourse to Brouwer 'over-lapping choice sequences' to get to something we might term 'context free'- i.e 'absolute'- with respect to its representation in this or that formal system.
Brouwer's constructivism, like Abhinavagupta's Dhvani, which gives rise to 'apurvata'- 'newness' in Reception- is of an intuitionistic, non-deterministic, type and exceeds computability or purely algorithmic methods.
I will argue, in my next post, that overlapping choice sequences naturally describe what is essentially a co-evolutionary fitness landscape and that the concepts of  apurvata and antarabhava gains salience in that context. My contention is that Paninian Sanskrit, yoked to the apophatic project of Gnosis, does indeed merit comparison, if not emulation, by current Research Programs in 'context free' formal languages.


Anonymous said...

"Older languages- like Latin or Old English- tend to be highly inflected and thus word-order doesn't matter. However the corruption of a single morpheme radically changes meaning so, in practice, both increased redundancy and loss of inflection feature in the evolution of Language."

Did Latin and Old English get there- that is the state of highly inflected morphology- also through linguistic evolution? If yes, is it true that the increasingly complicated inflection constitutes a lowering of entropy? Do you think that this process may have been intentional- were people deliberately making their grammar more inflected to serve some purpose?

windwheel said...

Entropy should increase if inflection is fusional because more information is getting compressed into a given character string. However, from the semantic point of view the opposite could be the case. Isolating languages like Chinese have higher entropy or Kolmogorov complexity. Agglutinative Persian, or Urdu 'ezafat' which just links two completely different words together without spelling out how they are related can exceed even polysynthetic languages in the quality of compression. Take 'kajdar-o-marez' as used by Iqbal- it means 'tilting the wine bottle in such a fashion that you appear to be generously filling the other person's glass but actually you are not letting even a drop flow'.
The point here is that there's on linear relationship between things like syntheticity/analyticity or fusional/agglutinatve etc/ tp deter,ome actual entropy. Still, if Chinese characters take longer to write, or if telegraph messages are more costly to send, then we would expect to see higher entropy for Chinese or telegraphese. In the latter case, newspaper reporters used the suffix '-wise' to compress word count and pay lower telegram charges. Some people argue that spoken English is becoming more inflected.
With liturgical or literary languages, clearly, both difficulty of composition and the cost of deciphering affect the fitness landscape. It makes sense for the 'i-language' speakers (i.e. those fluent in its expression) to have two or three different models in their head so that 'e-language' (i.e. what is heard or read) can have higher entropy without sacrificing fail-safe redundancy. On the one hand this means that 'collocations' or 'merisms' rather than words gain salience. One word suggests the one it is associated with. Panini himself uses this feature to get high Kolmogorov complexity without loss of robustness.
Another way of thinking of robustness has to do with epigenetic canalisation- i.e. the ability of a system to produce the same observable result from different configurations.
Here too we find a result militating against linear relationships between type of grammar and the entropy of the E language- viz Shannon's Source coding theorem.
Returning to your question, it may be that high inflection makes oratory more effective because it becomes more personal- i.e. we will expect to see it in thymotic Tribal Republics- however for legal scribes and bureaucrats the sort of passive construction we see in Classical Sanskrit is preferable. Auerbach, in 'Mimesis' has many texts illustrating notions like this however they are specific to Europe where military conquest was the primary motive force of cultural change.
In India, by contrast, Sanskrit spread by providing a peaceful solution to a Social co-ordination problem. It was not unique in this. What was unique is the manner in which it survived and regenerated itself without explicit support from either the State or the Market. amazingly, Religions which denied it any special place- e.g. Jainism and Buddhism- became vectors for its propagation. I should add, it was never the monopoly of some caste or Priestly cabal or bunch of aristocratic gangsters.
It is a mistake to think the Indians went crazy about linguistics and neglected everything else. On the contrary, their interest in combinatorics and discrete maths for decision theory went hand in hand with their development of algorithmic methods in linguistics. Umaswati is a good example of a Maths guy turned Theological writer. he is referencing thermodynamic notions as well as 'matching problems' in the Jain context such that Advaita and Madhyamika become observationally indistinguishable from his own orthodoxy.
The true greatness of Panini and Patanjali and so on lies in the fact that they saw that human problems have non-coercive, egalitarian, co-operative solutions.

windwheel said...

Sadly, Indologists nowadays promote the notion that Hinduism is some sort of Nazism. Just as the Nazis had some good rocket scientists to spread their evil, so too did these evil 'Brahmins' have a secret weapon in the shape of Panini.
This is utterly foolish.
At one time, people believed in 'strong A.I'. Worse they thought that Language itself was some sort of Evil, Hegemonic force which turned its speakers into robots. Maths has progressed since then.
There is a very good blog by Bhupinder Singh Anand on putting Maths on the foundations of computability- i.e. making it the servant not the potential master of Humanity. Anand is not a Professor or getting any money from his research. He is typical of the large class of Indian people who have always existed whose labor is one of love, not academic politics.
Another inspiring example of this continuity in Indian culture is the 'Shataavadhani' Ganesh.
Such people understand that Knowledge is free for all who have interest in it. It is not something to be bought and sold.

Anonymous said...

'The point here is that there's on linear relationship between things like syntheticity/analyticity or fusional/agglutinatve etc/ tp deter,ome actual entropy'
Kindly clarify

windwheel said...

that should be 'the point here is that there is no linear relationship between things like syntheticity/analyticity or fusional/agglutinative etc such that actual entropy can be algorithmically determined in advance.'
Thank you for your comment.